Example 1 Let \(G:=(\mathbb {Z}/p^2\mathbb {Z},+,\circ )\)  be the skew left braces given by \(a\circ b:=a+b+pab\)  for all \(a,b\in \mathbb {Z}/p^2\mathbb {Z}\)  and \(E\)  the trivial left semi-brace on \(\mathbb {Z}/p\mathbb {Z}\) . Let \(B\)  be the left semi-brace given by \(B:=G\rtimes _{\alpha } E\)  where \(\alpha :E\longrightarrow Aut(G,+,\circ )\)  is given by \(\alpha _e(g):=(1+pe)g\)  for all \(e\in E\) , \(g\in G\) . By leftnilpo \(B\)  is a left nilpotent left cancellative semi-brace. On the other hand, \(E\)  is not contained in the centralizer of \(G\)  and it is not a normal subgroup of \((B,\circ )\)  hence it can not be constructed by [1]}.

